Some Inequalities between General Randić-Type Graph Invariants

The Randić-type graph invariants are extensively investigated vertex-degree-based topological indices and have gained much prominence in recent years. The general Randić and zeroth-order general Randić indices are Randić-type graph invariants and are defined for a graph with vertex set as and , respectively, where is an arbitrary real number, denotes the degree of a vertex , and represents the adjacency of vertices and in . Establishing relationships between two topological indices holds significant importance for researchers. Some implicit inequality relationships between and have been derived so far. In this paper, we establish explicit inequality relationships between and . Also, we determine linear inequality relationships between these graph invariants. Moreover, we obtain some new inequalities for various vertex-degree-based topological indices by the appropriate choice of .